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Kent, you wrote:
"Sun SD: 15m 45s
Moon SD: 15m 25s
Moon HP: 56m 36s"

These are fine. Incidentally, you can also check this sort of thing on my
web site (see below).

And:
"For my GMT 06-25-51 the values according to Umland shall be:
Sun SD: 15m 45,1s (USNO 15m 48s)
Moon SD: 15m 25,5s (USNO 15m 36s)
Moon HP: 56m 36,5s."

Who is Umland, incidentally? I notice that you have gotten in the habit of
quoting things to a FRACTION of a SECOND of arc. You don't need anywhere
near that level of detail, especially since you say you're trying to do
things the way a 19th century navigator would have done things.

Andyou wrote:
"My augmentation in the moon's altitude reduction was -12,96s. Minus because
the UL was observed."

Well, now, that right there could explain a whole lot. The augmentation is
ALWAYS positive. It's true that you would subtract that quantity from an
upper limb altitude sight, but that's because it's adding onto the Moon's
semi-diameter, and the fact that it was an upper limb obs is really
irrelevant to the rest.

And you wrote:
"This figure also includes a small correction for refraction of +0,34s."

There is no reason to include such miniscule effects. Clearing lunars is
EASY. I think you're getting carried away with minor details.

And:
"My moon parallax incl. corrections for earth flattening was 26m 50,39s. It
is not clear to me how George corrects for earth flattening."

The discrepancy between your clearing and George's (and everybody else's!)
has nothing to do with the oblateness of the Earth (earth flattening). This
is always a very minor factor. It can be ignored in lunar distance problems,
and when it is, on average it will lead to an error in position of only
about one nautical mile, occasionally as much as three nautical miles.
That's all.

And:
"The angles between the distance line and the verticals were not calculated
by me"

Yes, but we KNOW that those angles were close to zero because Jeremy
described his observation and said that the Sun and Moon were on opposite
sides of the sky. And as I noted in another post, this simple alignment
means that the whole lunar observation can be cleared without using any trig
at all. Lunars are easy.

And:
"and therefore I did not put in any corrections for:- the decrease of SD's
in my distance reduction. The altitude of the moon is high and does not
require any correction. The sun can be corrected with -1s."

In case anyone else is following along and trying to understand what Kent is
describing, this is "refractional flattening" of the visible shape of the
Sun or Moon in the sky. Basically this is a correction to the object's
apparent semi-diameter. But it is exceedingly small unless the Sun or Moon
are below about 12 degrees altitude. It can be ignored without any serious
consequences (except when the object is very low in the sky).

And you wrote:
"the moon's parallax in azimuth. If I do a calculation of these angles this
correction is -0,74s (moon in E and sun to the right
seen by the observer). These angles are small (8 and 13 degr respectively).
Anyway, the exclusion of these two small corrections will have minor impact
on the final LD."

If you really want to deal with the small changes in the Moon's position due
to oblateness, I recommend you use the method in Chauvenet. Then you can
drop all talk of "parallax in azimuth". The corrections are simple. But
again, just as you say, this is a trivial matter and it would not change
anything in the case under consideration.

Kent, have you tried the lunars clearing calculator on my web site?
 http://www.HistoricalAtlas.com/lunars
Click on "Clear a Lunar Online" You can easily experiment with different
lunar observations. There are checkboxes that let you include or ignore the
corrections for oblateness of the Earth and refractional flattening. By
toggling these, you can see very quickly that they are usually minor
corrections. Nothing you need to fuss over. And in addition, it is highly
unlikely that any real navigator at sea would have applied the oblateness
correction. This is an "armchair navigator's" detail.

 -FER

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